Olber's Paradox for Superluminal Neutrinos: Constraining Extreme Neutrino Speeds at TeV-ZeV Energies with the Diffuse Neutrino Background

TL;DR

This paper uses the non-detection of diffuse astrophysical neutrino backgrounds to set upper limits on superluminal neutrino speeds at TeV-ZeV energies, challenging certain superluminal neutrino hypotheses.

Contribution

It introduces a novel method to constrain superluminal neutrino speeds by analyzing the brightness of the diffuse neutrino background and comparing it with observational limits.

Findings

Limits on v/c: <= 820 at 60 TeV

Constraints: v/c < 2500 at 0.1 EeV, < 4.6 at 4 EeV

Inconsistent with naive extrapolation of OPERA results

Abstract

The only invariant speed in special relativity is c; therefore, if some neutrinos travel at even tiny speeds above c, normal special relativity is incomplete and any superluminal speed may be possible. I derive a limit on superluminal neutrino speeds v >> c at high energies by noting that such speeds would increase the size of the neutrino horizon. The increased volume of the Universe visible leads to a brighter astrophysical neutrino background. The nondetection of "guaranteed" neutrino backgrounds from star-forming galaxies and ultrahigh energy cosmic rays (UHECRs) constrains v/c at TeV--ZeV energies. I find that v/c <= 820 at 60 TeV from the nondetection of neutrinos from star-forming galaxies. The nondetection of neutrinos from UHECRs constrains v/c to be less than 2500 at 0.1 EeV in a pessimistic model and less than 4.6 at 4 EeV in an optimistic model. The UHECR neutrino background nondetection is strongly inconsistent with a naive quadratic extrapolation of the OPERA results to EeV energies. The limits apply subject to some caveats, particularly that the expected pionic neutrino backgrounds exist and that neutrinos travel faster than c when they pass the detector. They could be improved substantially as the expected neutrino backgrounds are better understood and with new experimental neutrino background limits. I also point out that extremely subluminal speeds would result in a much smaller neutrino background intensity than expected.